This activity involves rounding four-digit numbers to the nearest thousand.
What happens when you round these three-digit numbers to the nearest 100?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
What happens when you round these numbers to the nearest whole number?
Find the sum of all three-digit numbers each of whose digits is
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
In this problem we are looking at sets of parallel sticks that
cross each other. What is the least number of crossings you can
make? And the greatest?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Can you explain how this card trick works?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
Delight your friends with this cunning trick! Can you explain how
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
Here are two kinds of spirals for you to explore. What do you notice?
Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
This task follows on from Build it Up and takes the ideas into three dimensions!
This challenge asks you to imagine a snake coiling on itself.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Can you dissect an equilateral triangle into 6 smaller ones? What
number of smaller equilateral triangles is it NOT possible to
dissect a larger equilateral triangle into?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Can you find all the ways to get 15 at the top of this triangle of numbers?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
Consider all two digit numbers (10, 11, . . . ,99). In writing down
all these numbers, which digits occur least often, and which occur
most often ? What about three digit numbers, four digit numbers. . . .
Find out what a "fault-free" rectangle is and try to make some of
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
An investigation that gives you the opportunity to make and justify
Are these statements always true, sometimes true or never true?
Start with any number of counters in any number of piles. 2 players
take it in turns to remove any number of counters from a single
pile. The winner is the player to take the last counter.
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable.
Decide which of these diagrams are traversable.
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
A collection of games on the NIM theme
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?